Existence and blow up for viscoelastic hyperbolic equations with variable exponents
In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then w...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-10-01
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| Series: | Communications in Analysis and Mechanics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024032 |
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| Summary: | In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then we prove that a solution blows up in finite time with positive initial energy as well as nonpositive initial energy. |
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| ISSN: | 2836-3310 |